Problem: The sum of two numbers is $109$, and their difference is $59$. What are the two numbers?
Solution: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 109}$ ${x-y = 59}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 168 $ $ x = \dfrac{168}{2} $ ${x = 84}$ Now that you know ${x = 84}$ , plug it back into $ {x+y = 109}$ to find $y$ ${(84)}{ + y = 109}$ ${y = 25}$ You can also plug ${x = 84}$ into $ {x-y = 59}$ and get the same answer for $y$ ${(84)}{ - y = 59}$ ${y = 25}$ Therefore, the larger number is $84$, and the smaller number is $25$.